Equivariant E-theory for C*-algebras
Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups E G(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C…
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- Full title :Equivariant E-theory for C*-algebras / Erik Guentner, Nigel Higson, Jody Trout.
Summary
Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups E G(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in recent work of Higson and Kasparov on the Baum-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space.
Read More ↓Edition Statements
- Publication Date:©2000.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©2000.
The Physical Object
- Description:1 online resource (viii, 86 pages)
Edition Identifiers
- ISBN:9781470402945, 1470402947
- oclc:ocn851088840
- LC Classification:QA3
- Dewey Decimal:510 s 514/.23
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